SEVERAL ITERATIVE SCHEMES FOR THE SPLIT FEASIBILITY WITH MULTIPLE OUTPUT SETS AND APPLICATIONS

Abstract

In this paper, for solving the split feasibility problem with multiple

output sets, defined by demiclosed strongly quasi-nonexpansive opera-

tors on Hilbert spaces, we propose some block-iterative schemes, using

the extrapolated Landweber-type operators. The strong convergence is

proved without the boundedly regular condition as well as the closedness

property of the range of the transformation operators, assumed recently

in the literature for the similar problems. We give a necessary and suf-

ficient condition which ensures that a kth iterate is a solution. We also

give an application of our results to solve the multiple-sets split feasibil-

ity problem (MSSFP) with multiple output level sets with computational

experiments for illustration.